Abstract
This article is devoted to introduce a new geometric constant called Dehghan–Rooin constant, which quantifies the difference between angular and skew angular distances in Banach spaces. We quantify the characterization of uniform non-squareness in terms of Dehghan–Rooin constant. The relationships between Dehghan–Rooin constant and uniform convexity, Dehghan-Rooin constant and uniform smoothness are also studied. Moreover, some new sufficient conditions for uniform normal structure are also established in terms of Dehghan–Rooin constant.
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This work was completed with the support of the National Natural Science Foundation of P. R. China (Nos. 11971493 and 12071491)
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Communicated by Constantin Niculescu.
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Fu, Y., Li, Y. Geometric constant for quantifying the difference between angular and skew angular distances in Banach spaces. Ann. Funct. Anal. 15, 39 (2024). https://doi.org/10.1007/s43034-024-00341-0
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DOI: https://doi.org/10.1007/s43034-024-00341-0
Keywords
- Angular distance
- Skew angular distance
- Uniform non-squareness
- Uniform convexity
- Uniform smoothness
- Uniform normal structure